# Scheduling an interval ordered precedence graph with communication delays and a limited number of processors

Alix Munier Kordon; Fadi Kacem; Benoît Dupont de Dinechin; Lucian Finta

RAIRO - Operations Research - Recherche Opérationnelle (2013)

- Volume: 47, Issue: 1, page 73-87
- ISSN: 0399-0559

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topKordon, Alix Munier, et al. "Scheduling an interval ordered precedence graph with communication delays and a limited number of processors." RAIRO - Operations Research - Recherche Opérationnelle 47.1 (2013): 73-87. <http://eudml.org/doc/275037>.

@article{Kordon2013,

abstract = {We consider the scheduling of an interval order precedence graph of unit execution time tasks with communication delays, release dates and deadlines. Tasks must be executed by a set of processors partitioned into K classes; each task requires one processor from a fixed class. The aim of this paper is to study the extension of the Leung–Palem–Pnueli (in short LPP) algorithm to this problem. The main result is to prove that the LPP algorithm can be extended to dedicated processors and monotone communication delays. It is also proved that the problem is NP–complete for two dedicated processors if communication delays are non monotone. Lastly, we show that list scheduling algorithm cannot provide a solution for identical processors.},

author = {Kordon, Alix Munier, Kacem, Fadi, Dupont de Dinechin, Benoît, Finta, Lucian},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {approximation and complexity; combinatorial optimization; scheduling},

language = {eng},

number = {1},

pages = {73-87},

publisher = {EDP-Sciences},

title = {Scheduling an interval ordered precedence graph with communication delays and a limited number of processors},

url = {http://eudml.org/doc/275037},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Kordon, Alix Munier

AU - Kacem, Fadi

AU - Dupont de Dinechin, Benoît

AU - Finta, Lucian

TI - Scheduling an interval ordered precedence graph with communication delays and a limited number of processors

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 1

SP - 73

EP - 87

AB - We consider the scheduling of an interval order precedence graph of unit execution time tasks with communication delays, release dates and deadlines. Tasks must be executed by a set of processors partitioned into K classes; each task requires one processor from a fixed class. The aim of this paper is to study the extension of the Leung–Palem–Pnueli (in short LPP) algorithm to this problem. The main result is to prove that the LPP algorithm can be extended to dedicated processors and monotone communication delays. It is also proved that the problem is NP–complete for two dedicated processors if communication delays are non monotone. Lastly, we show that list scheduling algorithm cannot provide a solution for identical processors.

LA - eng

KW - approximation and complexity; combinatorial optimization; scheduling

UR - http://eudml.org/doc/275037

ER -

## References

top- [1] H.H. Ali and H.H. El.-Rewini, An optimal algorithm for scheduling interval ordered tasks with communication on processors. J. Comput. Syst. Sci. 2 (1995) 301–307. Zbl0830.68007MR1356508
- [2] P. Chrétienne and C. Picouleau, Scheduling with communication delays : a survey. in Scheduling Theory and its Applications, edited P. Chrétienne, E.G. Coffman, J.K. Lenstra and Z. Liu. John Wiley Ltd (1995) 65–89. MR1376609
- [3] B. Dupont de Dinechin, Scheduling monotone interval orders on typed task systems. In PLANSIG 2007, 26th Worshop of the UK Planning and Scheduling Special Interest Group (2007) 25–31.
- [4] R. Giroudeau, J.-C. Konig, F.K. Moulai and J. Palaysi, Complexity and approximation for precedence constrained scheduling problems with large communication delays. Theor. Comput. Sci.401 (2008) 107–119. Zbl1143.90012MR2431829
- [5] W. Horn, Some simple scheduling algorithms. Naval Research Logistics Quarterly21 (1974) 177–185. Zbl0276.90024MR343895
- [6] J. Hwang, Y. Chow, F. Anger and C. Lee, Scheduling precedence graphs in systems with interprocessor communication times. SIAM J. Comput.18 (1989) 244–257. Zbl0677.68026MR986664
- [7] K. Jansen, Analysis of Scheduling Problems with Typed Task Systems. Discrete Appl. Math.52 (1994) 223–232. Zbl0822.90083MR1287973
- [8] A. Leung, K.V. Palem and A. Pnueli, Scheduling Time-Constrained Instructions on Pipelined Processors. ACM Transact. Program. Languages Syst.23 (2001) 73–103.
- [9] K. Palem and B. Simons, Scheduling time-critical instructions on risc machines. ACM Transactions on Programming Languages and Systems4 (1993) 632–658.
- [10] C.H Papadimitriou and M. Yannakakis, Scheduling interval-ordered tasks. SIAM J. Comput.8 (1979) 405–409. Zbl0421.68040MR539257
- [11] B. Veltman, B.J. Lageweg and J.K. Lenstra, Multiprocessor scheduling with communication delays. Parallel Comput.16 (1990) 173–182. Zbl0711.68017
- [12] J. Verriet, The complexity of scheduling typed task systems with and without communication delays. External Report 1998-26, UU-CS (1998).
- [13] J. Verriet, Scheduling interval-ordered tasks with non-uniform deadlines subject to non-zero communication delays. Parallel Comput.25 (1999) 3–21. Zbl0914.68014MR1675126
- [14] W. Yu, H. Hoogeveen and J.K. Lenstra, Minimizing makespan in a two-machine flow shop with delays and unit-time operations is np-hard. J. Scheduling7 (2004) 333–348. Zbl1154.90506MR2101693

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